A benchmark generator for dynamic multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Many real-world optimization problems appear to not only have multiple objectives that conflict each other but also change over time. They are dynamic multi-objective optimization problems (DMOPs) and the corresponding field is called dynamic multi-objective optimization (DMO), which has gained growing attention in recent years. However, one main issue in the field of DMO is that there is no standard test suite to determine whether an algorithm is capable of solving them. This paper presents a new benchmark generator for DMOPs that can generate several complicated characteristics, including mixed Pareto-optimal front (convexity-concavity), strong dependencies between variables, and a mixed type of change, which are rarely tested in the literature. Experiments are conducted to compare the performance of five state-of-the-art DMO algorithms on several typical test functions derived from the proposed generator, which gives a better understanding of the strengths and weaknesses of these tested algorithms for DMOPs

Evolutionary Algorithms for Static and Dynamic Multiobjective Optimization

Many real-world optimization problems consist of a number of conflicting objectives that have to be optimized simultaneously. Due to the presence of multiple conflicting ob- jectives, there is no single solution that can optimize all the objectives. Therefore, the resulting multiobjective optimization problems (MOPs) resort to a set of trade-off op- timal solutions, called the Pareto set in the decision space and the Pareto front in the objective space. Traditional optimization methods can at best find one solution in a sin- gle run, thereby making them inefficient to solve MOPs. In contrast, evolutionary algo- rithms (EAs) are able to approximate multiple optimal solutions in a single run. This strength makes EAs good candidates for solving MOPs. Over the past several decades, there have been increasing research interests in developing EAs or improving their perfor- mance, resulting in a large number of contributions towards the applicability of EAs for MOPs. However, the performance of EAs depends largely on the properties of the MOPs in question, e.g., static/dynamic optimization environments, simple/complex Pareto front characteristics, and low/high dimensionality. Different problem properties may pose dis- tinct optimization difficulties to EAs. For example, dynamic (time-varying) MOPs are generally more challenging than static ones to EAs. Therefore, it is not trivial to further study EAs in order to make them widely applicable to MOPs with various optimization scenarios or problem properties. This thesis is devoted to exploring EAs’ ability to solve a variety of MOPs with dif- ferent problem characteristics, attempting to widen EAs’ applicability and enhance their general performance. To start with, decomposition-based EAs are enhanced by incorpo- rating two-phase search and niche-guided solution selection strategies so as to make them suitable for solving MOPs with complex Pareto fronts. Second, new scalarizing functions are proposed and their impacts on evolutionary multiobjective optimization are exten- sively studied. On the basis of the new scalarizing functions, an efficient decomposition- based EA is introduced to deal with a class of hard MOPs. Third, a diversity-first- and-convergence-second sorting method is suggested to handle possible drawbacks of convergence-first based sorting methods. The new sorting method is then combined with strength based fitness assignment, with the aid of reference directions, to optimize MOPs with an increase of objective dimensionality. After that, we study the field of dynamic multiobjective optimization where objective functions and constraints can change over time. A new set of test problems consisting of a wide range of dynamic characteristics is introduced at an attempt to standardize test environments in dynamic multiobjective optimization, thereby aiding fair algorithm comparison and deep performance analysis. Finally, a dynamic EA is developed to tackle dynamic MOPs by exploiting the advan- tages of both generational and steady-state algorithms. All the proposed approaches have been extensively examined against existing state-of-the-art methods, showing fairly good performance in a variety of test scenarios. The research work presented in the thesis is the output of initiative and novel attempts to tackle some challenging issues in evolutionary multiobjective optimization. This re- search has not only extended the applicability of some of the existing approaches, such as decomposition-based or Pareto-based algorithms, for complex or hard MOPs, but also contributed to moving forward research in the field of dynamic multiobjective optimiza- tion with novel ideas including new test suites and novel algorithm design

A steady-state and generational evolutionary algorithm for dynamic multi-objective optimization

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods

Evolutionary Dynamic Multi-Objective Optimisation : A survey

Peer reviewedPostprin

Solving dynamic multi-objective problems with a new prediction-based optimization algorithm

Funding Information: This work is supported by the National Natural Science Foundation of China under Grants 62006103 and 61872168, in part by the Jiangsu national science research of high education under Grand 20KJB110021. The authors express sincerely appreciation to the anonymous reviewers for their helpful opinions.Peer reviewedPublisher PD

NIHBA : A network interdiction approach for metabolic engineering design

Funding Information: This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) for funding project ‘Synthetic Portabolomics: Leading the way at the crossroads of the Digital and the Bio Economies (EP/N031962/1)’. N.K. was funded by a Royal Academy of Engineering Chair in Emerging Technology award.Peer reviewedPublisher PD

Scalarizing Functions in Decomposition-Based Multiobjective Evolutionary Algorithms

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm

Approximating Multiobjective Optimization Problems with Complex Pareto Fronts

The file attached to this record is the author's final peer reviewed version.The main goal of multiobjective optimization is to achieve a set of well-converged and evenly-distributed Pareto optimal points. While evolutionary algorithms have been reported to converge well, their distribution performance might not be as uniform as we expected, especially when the problems to be optimized involve complex Pareto fronts. In this paper, with the aid of a set of uniformly-distributed reference points, multiobjective optimization problems (MOPs) can be handled by minimizing least reference distances (LRD), which measure the proximity of solutions to their nearest reference points. This way, the uniformity of approximated solutions is implicitly controlled by the reference point set, and convergence is in the charge of LRD. The proposed LRD algorithm (LRDA) is tested and compared with several popular algorithms on a number of old and newly-developed MOPs that have complex Pareto fronts, showing that this method is very promising to obtain evenly-distributed Pareto optimal points for the problems considered in this paper

A Fast Strength Pareto Evolutionary Algorithm Incorporating Predefined Preference Information

Strength Pareto Evolutionary Algorithm 2 (SPEA2) has achieved great success for handling multiobjective optimization problems. However, it has been widely reported that SPEA2 gets subjected to a huge amount of computational effort while pursuing a good distribution of approximated solutions. This paper explores a new way to keep the good properties of SPEA2 and reduce its high computational burden simultaneously, with the aid of predefined preference information. By incorporating preference information, the proposed fast SPEA (FSPEA) can efficiently perform individuals' density estimation and environmental selection, thus speeding up the whole running time of the evolution process. Empirical studies show that the proposed FSPEA algorithm can obtain very competitive performance on a number of multiobjective test problems considered in this paper

A strength pareto evolutionary algorithm based on reference direction for multiobjective and many-objective optimization

While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference directionbased density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization